Generate restricted weak integer compositions (or partitions) of an integer n into k parts in Python

问题

(Re-posting, as I did not get any response to my previous post)
I am trying to write a Python code to generate weak integer compositions (partitions) of a number 'n' into 'k' parts but with a MINIMUM and MAXIMUM value constraint on each partition (see example given below). Also, the partitions have to be generated in lexicographic order. I have found some related posts but have not been able to implement it. Any help will be appreciated.

Example:
Possible integer partitions for n=5 in k=3 parts:
[5,0,0], [4,1,0], [4,0,1], [3,2,0], [3,1,1], [3,0,2], ..., [0,0,5]
After imposing the constraint that each integer in the partition has a MINIMUM value 0 and a MAXIMUM value 3, I should get:
[3,2,0], [3,1,1], [3,0,2], ...so on, only.

Related posts:
Elegant Python code for Integer Partitioning
Generate lexicographic series efficiently in Python

回答1:

This kind of problem is most straightforward to solve with a recursive generator function. To generate partitions of n into k parts, we can select the first part v, and then recursively partition n - v into k - 1 parts.

You want earlier solutions to have larger numbers in the first position, so we'll choose v in descending order.

def constrained_partitions(n, k, min_elem, max_elem):
    allowed = range(max_elem, min_elem-1, -1)

    def helper(n, k, t):
        if k == 0:
            if n == 0:
                yield t
        elif k == 1:
            if n in allowed:
                yield t + (n,)
        elif min_elem * k <= n <= max_elem * k:
            for v in allowed:
                yield from helper(n - v, k - 1, t + (v,))

    return helper(n, k, ())

Example:

>>> for p in constrained_partitions(5, 3, 0, 3):
...     print(p)
... 
(3, 2, 0)
(3, 1, 1)
(3, 0, 2)
(2, 3, 0)
(2, 2, 1)
(2, 1, 2)
(2, 0, 3)
(1, 3, 1)
(1, 2, 2)
(1, 1, 3)
(0, 3, 2)
(0, 2, 3)

来源：https://stackoverflow.com/questions/58915599/generate-restricted-weak-integer-compositions-or-partitions-of-an-integer-n-in